Custom penalties for PELT

[rnagabhyrava]

Hey guys,

First of all, I am new to changepoint detection and this package has helped me a lot. Love your work and thank you for all the time and effort you put into this.

Coming to my question, I am working with PELT and various costs (l1, l2, normal). I am confused about what penalties to use with for each of these. I believe we can use AIC/BIC (correct me if wrong), as you mentioned here this bic formula only applies for l2. Can someone help me with what penalty/formula goes with each of l1, l2 and normal with PELT?

Thanks,
rnaga

[deepcharles]

Sorry for the late reply.

To compute the BIC criterion, you need to plug in the definition the correct likelihood function and maximum likelihood estimator.

Using the Gaussian likelihood (with fixed variance) yields the BIC formula for the L2 cost function.
Using the Gaussian likelihood (with varying variance) yields the BIC formula for the normal cost function.
You can refer to this book for the computation of the maximum likelihood for several likelihood functions.

In BIC, the number of parameters (denoted k in the Wikipedia formula) is usually proportional to the number of change points and the signal dimension.

As for the L1 cost function, I am not sure there is a BIC that can be derived.

Hope that helps